Do I really need a visa to perform an internship in the U.S.?

Yes. You need a valid J-1 visa covering the entire period of your internship or training in the US. The J-1 visa allows you to legally participate as well as to reside in the US for the duration of your internship/training. Without the J-1 visa you cannot enter in the USA and cannot start your internship.

Please be aware that the J-1 visa is tied to a specific host organization and can only be issued for one explicit, previously approved internship or training. Once you are in the U.S., you can only change your host company or make adjustments to your internship or training length under very limited circumstances, and only after approval.